Prime Factorization of 280

Oct 13, 2025 by leolavanderia.com.br 6 views

Introduction

In mathematics, factors and multiples are fundamental concepts that help us understand the properties of numbers. Factors are the numbers that divide a given number without leaving a remainder, while multiples are the products of a given number and an integer. In this article, we will explore the smallest factor of 280 and the first three multiples of 280.

What is the Smallest Factor of 280?

To find the smallest factor of 280, we need to identify the smallest number that divides 280 without leaving a remainder. We can start by listing the factors of 280.

Factors of 280:

As we can see, the smallest factor of 280 is 1. This is because 1 is the only number that divides 280 without leaving a remainder.

What are the First Three Multiples of 280?

To find the first three multiples of 280, we need to multiply 280 by the first three positive integers.

Multiples of 280:

280 × 1 = 280
280 × 2 = 560
280 × 3 = 840

Therefore, the first three multiples of 280 are 280, 560, and 840.

Prime Factorization of 280

To understand the properties of 280, we need to find its prime factorization. The prime factorization of 280 is:

280 = 2^3 × 5 × 7

This means that 280 can be expressed as the product of three prime numbers: 2, 5, and 7.

Importance of Factors and Multiples

Factors and multiples are essential concepts in mathematics that have numerous applications in real-life situations. For example, in finance, factors and multiples are used to calculate interest rates and investment returns. In science, factors and multiples are used to measure the properties of physical quantities such as length, mass, and time.

Real-World Applications of Factors and Multiples

Factors and multiples have numerous real-world applications in various fields such as:

Finance: Factors and multiples are used to calculate interest rates, investment returns, and stock prices.
Science: Factors and multiples are used to measure the properties of physical quantities such as length, mass, and time.
Engineering: Factors and multiples are used to design and optimize systems such as bridges, buildings, and electronic circuits.
Computer Science: Factors and multiples are used in algorithms and data structures to solve complex problems.

Conclusion

In conclusion, the smallest factor of 280 is 1, and the first three multiples of 280 are 280, 560, and 840. The prime factorization of 280 is 2^3 × 5 × 7. Factors and multiples are essential concepts in mathematics that have numerous applications in real-life situations. Understanding factors and multiples is crucial for solving complex problems in various fields such as finance, science, engineering, and computer science.

Frequently Asked Questions

What is the smallest factor of 280?
- The smallest factor of 280 is 1.
What are the first three multiples of 280?
- The first three multiples of 280 are 280, 560, and 840.
What is the prime factorization of 280?
- The prime factorization of 280 is 2^3 × 5 × 7.

References

[1] Khan Academy. (n.d.). Factors and Multiples. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-and-multiples
[2] Math Open Reference. (n.d.). Factors and Multiples. Retrieved from https://www.mathopenref.com/factorsmultiples.html
[3] Wolfram MathWorld. (n.d.). Factors and Multiples. Retrieved from https://mathworld.wolfram.com/FactorsandMultiples.html

Introduction

In our previous article, we explored the smallest factor of 280 and the first three multiples of 280. We also discussed the importance of factors and multiples in various fields such as finance, science, engineering, and computer science. In this article, we will answer some frequently asked questions about factors and multiples.

Q&A: Factors and Multiples

Q: What is the difference between a factor and a multiple?

A: A factor is a number that divides another number without leaving a remainder, while a multiple is the product of a number and an integer.

Q: How do I find the factors of a number?

A: To find the factors of a number, you can list all the numbers that divide the given number without leaving a remainder. Alternatively, you can use the prime factorization method to find the factors.

Q: What is the prime factorization method?

A: The prime factorization method involves expressing a number as the product of its prime factors. For example, the prime factorization of 280 is 2^3 × 5 × 7.

Q: How do I find the multiples of a number?

A: To find the multiples of a number, you can multiply the number by the first few positive integers. For example, the first three multiples of 280 are 280, 560, and 840.

Q: What is the relationship between factors and multiples?

A: Factors and multiples are related in that the product of a number and its factors is equal to the number itself. For example, the product of 280 and its factors is 280.

Q: Can a number have more than one factor?

A: Yes, a number can have more than one factor. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Q: Can a number have more than one multiple?

A: Yes, a number can have more than one multiple. For example, the multiples of 12 are 12, 24, 36, 48, 60, and so on.

Q: What is the smallest factor of a number?

A: The smallest factor of a number is 1, as 1 is the only number that divides any number without leaving a remainder.

Q: What is the largest factor of a number?

A: The largest factor of a number is the number itself, as the number is always a factor of itself.

Q: Can a number have a factor that is greater than the number itself?

A: No, a number cannot have a factor that is greater than the number itself, as the factor would then be the number itself.

Q: Can a number have a multiple that is less than the number itself?

A: No, a number cannot have a multiple that is less than the number itself, as the multiple would then be a factor of the number.

Conclusion

In conclusion, factors and multiples are essential concepts in mathematics that have numerous applications in real-life situations. Understanding factors and multiples is crucial for solving complex problems in various fields such as finance, science, engineering, and computer science. We hope that this article has helped to clarify some of the frequently asked questions about factors and multiples.

Frequently Asked Questions: Factors and Multiples

What is the difference between a factor and a multiple?
- A factor is a number that divides another number without leaving a remainder, while a multiple is the product of a number and an integer.
How do I find the factors of a number?
- To find the factors of a number, you can list all the numbers that divide the given number without leaving a remainder. Alternatively, you can use the prime factorization method to find the factors.
What is the prime factorization method?
- The prime factorization method involves expressing a number as the product of its prime factors.
How do I find the multiples of a number?
- To find the multiples of a number, you can multiply the number by the first few positive integers.

References

[1] Khan Academy. (n.d.). Factors and Multiples. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-and-multiples
[2] Math Open Reference. (n.d.). Factors and Multiples. Retrieved from https://www.mathopenref.com/factorsmultiples.html
[3] Wolfram MathWorld. (n.d.). Factors and Multiples. Retrieved from https://mathworld.wolfram.com/FactorsandMultiples.html